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Saturn’s magnetospheres, and their identification on
closed equatorial field lines
S. V. Badman, S. W. H. Cowley
To cite this version:
S. V. Badman, S. W. H. Cowley. Significance of Dungey-cycle flows in Jupiter’s and Saturn’s
mag-netospheres, and their identification on closed equatorial field lines. Annales Geophysicae, European
Geosciences Union, 2007, 25 (4), pp.941-951. �hal-00318312�
www.ann-geophys.net/25/941/2007/ © European Geosciences Union 2007
Annales
Geophysicae
Significance of Dungey-cycle flows in Jupiter’s and Saturn’s
magnetospheres, and their identification on closed equatorial field
lines
S. V. Badman and S. W. H. Cowley
Department of Physics & Astronomy, University of Leicester, Leicester LE1 7RH, UK
Received: 29 September 2006 – Revised: 27 February 2007 – Accepted: 6 April 2007 – Published: 8 May 2007
Abstract. We consider the contribution of the solar
wind-driven Dungey-cycle to flux transport in Jupiter’s and Sat-urn’s magnetospheres, the associated voltages being based on estimates of the magnetopause reconnection rates recently derived from observations of the interplanetary medium in the vicinity of the corresponding planetary orbits. At Jupiter, the reconnection voltages are estimated to be ∼150 kV dur-ing several-day weak-field rarefaction regions, increasdur-ing to ∼1 MV during few-day strong-field compression regions. The corresponding values at Saturn are ∼25 kV for rarefac-tion regions, increasing to ∼150 kV for compressions. These values are compared with the voltages associated with the flows driven by planetary rotation. Estimates of the rota-tional flux transport in the “middle” and “outer” magneto-sphere regions are shown to yield voltages of several MV and several hundred kV at Jupiter and Saturn respectively, thus being of the same order as the estimated peak Dungey-cycle voltages. We conclude that under such circumstances the Dungey-cycle “return” flow will make a significant con-tribution to the flux transport in the outer magnetospheric re-gions. The “return” Dungey-cycle flows are then expected to form layers which are a few planetary radii wide inside the dawn and morning magnetopause. In the absence of signif-icant cross-field plasma diffusion, these layers will be char-acterized by the presence of hot light ions originating from either the planetary ionosphere or the solar wind, while the inner layers associated with the Vasyliunas-cycle and middle magnetosphere transport will be dominated by hot heavy ions originating from internal moon/ring plasma sources. The temperature of these ions is estimated to be of the order of a few keV at Saturn and a few tens of keV at Jupiter, in both layers.
Keywords. Magnetospheric physics (Magnetospheric
con-figuration and dynamics; Planetary magnetospheres; Plasma convection; Solar wind-magnetosphere interactions)
Correspondence to: S. V. Badman
(svb4@ion.le.ac.uk)
1 Introduction
Experimental investigation of the large-scale structure and dynamics of the magnetospheres of Jupiter and Saturn have become possible in recent years through data obtained both by spacecraft in situ and by remote-sensing instruments. The Galileo orbiter mission has been the principal source of in situ data at Jupiter (e.g. Krupp et al., 2001; Frank et al., 2002; Kronberg et al., 2005; Waldrop et al., 2005), as well as pro-viding remote sensing observations using radio emissions (e.g. Louarn et al., 2000). A similar body of information is currently being gathered at Saturn by the Cassini orbiter (e.g. Bunce et al., 2005; Dougherty et al., 2005; Gurnett et al., 2005; Young et al., 2005), now also including en-ergetic neutral atom imaging of magnetospheric dynamics (e.g. Krimigis et al., 2005; Paranicas et al., 2005). Informa-tion on global dynamics can also be obtained from studies of polar UV auroras observed by the Hubble Space Telescope (HST), at both Jupiter (e.g. Grodent et al., 2003a, b; Nichols et al., 2007) and Saturn (e.g. G´erard et al., 2004; Clarke et al., 2005; Grodent et al., 2005; Badman et al., 2005). The observed auroral emissions relate both to precipitation from hot plasma populations produced within the magneto-sphere, and to intense structured field-aligned current sys-tems that are associated with magnetosphere-ionosphere mo-mentum transfer (Cowley et al., 2004a, b, 2005a, b; Gustin et al., 2004, 2006; Nichols and Cowley, 2004; Jackman and Cowley, 2006).
From a theoretical viewpoint, two major aspects of large-scale dynamics must be considered, together with their mu-tual interaction. The first is the dynamics of the flow driven by the rotation of the planet through ion-neutral collisions in the ionosphere, combined with internal sources of plasma deriving from moon atmospheres and surfaces, and from ring grains. Such plasma is picked up by the rotational flow in the inner regions of the magnetosphere, transported outward by centrifugal action, and then lost by some process acting in the outer magnetosphere (Hill, 1979; Siscoe and Sum-mers, 1981; Hill et al., 1983; Southwood and Kivelson, 1989;
X X X X X X X X X X X X Sub-corotating “Hill region” Vasyliunas-cycle flows Dusk Dawn Sun Dungey-cycle tail x-line Vasyliunas-cycle tail X-line Dungey-cycle return flow Dungey-cycle magnetopause X-line O P
Fig. 1. Sketch of the flows in the jovian equatorial plane, with the
direction toward the Sun at the bottom of the figure, dawn to the left, and dusk to the right. Solid lines with arrows show plasma stream-lines, while dashed lines with arrows show streamlines which sep-arate flow regions with differing origins and characteristics as indi-cated. Dashed lines with “X”s indicate X-type reconnection lines, while the solid line marked “O” indicates the O-type line of the Vasyliunas-cycle plasmoid which is ejected down-tail (which is a streamline). The dot-dashed line marked “P” is the outer boundary of the plasmoid, which asymptotes to the dusk tail magnetopause (from Cowley et al., 2003b).
Pontius, 1997; Bespalov et al., 2006). Vasyliunas (1983) sug-gested that mass-loaded flux tubes in the outer corotating region will generally be radially restrained on the dayside by the solar wind dynamic pressure, but may then stretch out down-tail as they rotate into the dusk sector, eventually pinching off to form a tailward-propagating plasmoid. The mass-reduced closed portions of these flux tubes then return to the dayside via dawn, where they again become mass-loaded by radial diffusion from the inner regions and stretch out once more as they rotate into the dusk sector. Here we refer to this process as the Vasyliuncycle. The second as-pect of magnetospheric dynamics is the cyclical flow driven by the interaction between the magnetosphere and the solar wind. Here we assume from evidence at Earth that the inter-action is mediated principally by magnetic reconnection oc-curing at the magnetopause, producing open flux tubes that are transported by the solar wind flow to the tail (e.g. Cowley et al., 2003a). The flux then returns sunward to the dayside following reconnection episodes in the tail to complete the transport cycle. This process was first described for the ter-restrial magnetosphere by Dungey (1961), and is referred to here as the Dungey-cycle. In this note we discuss the relative magnitudes of the flux transport by rotational and Dungey-cycle dynamics in Jupiter’s and Saturn’s magnetosphere, and indicate how the contribution of the Dungey-cycle may po-tentially be identified in equatorial flows. In the next section we discuss the nature of the overall flow system before
es-timating the contributions from the rotational and Dungey-cycle flows in following sections.
2 Equatorial flows
Conceptual models of the large-scale magnetospheric field and flow containing both rotational/Vasyliunas-cycle and Dungey-cycle systems have been discussed for Jupiter by Cowley et al. (1996, 2003b), and for Saturn by Cowley et al. (2004a). A central purpose of these models was to show how the two flow systems can co-exist on a continuous basis. The equatorial flow in the jovian model discussed by Cow-ley et al. (2003b) is sketched in Fig. 1, and forms the basis of the discussion given here; the flow in the Saturn model is essentially similar. In Fig. 1 we look down onto the mag-netospheric equatorial plane from the north, with the direc-tion towards the Sun at the bottom of the diagram, dawn to the left, and dusk to the right. The solid lines with arrows show plasma streamlines, with three regimes of flow being depicted following the above discussion, which are separated by the dashed-line streamlines. The inner region is domi-nated by the production and pick-up of plasma from inter-nal sources (principally Io at Jupiter) by the rotating flow, followed by its outward radial transport through small-scale “diffusive” motions not depicted in the figure. The flow is near-rigidly corotating with the planet in the innermost re-gion, but as a consequence of outward transport, increasingly departs towards lower angular velocities at increasing dis-tances (e.g. Hill, 1979; Pontius, 1997; Cowley et al., 2002). This region is then surrounded by a flow layer where the flux tubes, still driven by planetary rotation, take part in the Vasyliunas-cycle. Here the closed mass-loaded flux tubes flow radially outward into the dusk tail before pinching-off to form a tailward-flowing plasmoid, as indicated above. The associated reconnection line and inner boundary of the plas-moid is indicated in the figure by the dashed line with “X”s, marked “Vasyliunas-cycle tail X-line”. The central O-type neutral line of the plasmoid is indicated by the line marked “O” (which is also a streamline), while the outer boundary of the plasmoid is indicated by the dot-dashed line marked “P” which eventually asymptotes to the dusk magnetopause.
The solar wind-generated flow in the figure, associated with the Dungey-cycle, is then confined to the dawn side of the system, where the “Dungey-cycle tail X-line” is lo-cated. Open tail flux tubes which are closed at this recon-nection site flow sunward to the dayside magnetopause in a layer adjacent to the dawn magnetopause, where (in the steady state) they become open once more due to reconnec-tion with the magnetosheath field. After this the open tubes become transported poleward out of the plane of the diagram, and then into the tail lobes due to the anti-sunward flow of the solar wind. Open flux tubes are then removed from the lobes at the reconnection site on the dawn side of the tail to complete the cycle. Flux tubes disconnected from the planet
at this site flow tailward on the dawn side of the tailward-propagating plasmoid. Overall, this picture shows that these large-scale plasma flow systems can co-exist on a continu-ous basis. It is nevertheless recognised that in reality both Vasyliunas-cycle and Dungey-cycle processes are likely to be time-dependent (e.g. Woch et al. 2004; Cowley et al., 2005a), and may also involve nightside flows that are more spatially structured than those depicted here, as speculated upon by Kivelson and Southwood (2005).
In terms of the observed plasma regions in Jupiter’s mag-netosphere, we suppose that the mass-loaded sub-corotating region corresponds to the jovian “middle magnetosphere”, which is dominated by the presence of an equatorial plasma-current sheet containing outwardly-diffusing cool iogenic plasma. We also suppose that the surrounding region of mass-reduced flux tubes flowing around the boundary via dawn from the Vasyliunas- and Dungey-cycle reconnection sites in the tail together form the “outer magnetosphere” region on the dayside, characterised by relatively strong southward-pointing fields in the equatorial plane and the lack of a central current sheet, as originally suggested by Cowley et al. (1996). In subsequent discussions Cowley et al. (2003b, 2005b) emphasised the Dungey-cycle contributions to this layer, while Kivelson and Southwood (2005) emphasise the Vasyliunas-cycle contribution. Here we will discuss in more detail the relative contributions of these two processes to the formation of the layer. We also recognise that the character of the layer will evolve as the plasma is transported from dawn around the dayside, due to reconnection-associated flux ero-sion at the magnetopause as depicted in Fig. 1, as well as to radial transport of plasma from the interior region (Kivelson and Southwood, 2005).
3 Rotational and Dungey-cycle flux transport at Jupiter and Saturn
It is evident from the above discussion that the flux transport driven by planetary rotation and by the Dungey-cycle will dominate in differing parts of the magnetosphere. Generally, rotation-driven flows will dominate in the inner regions of closed field lines, while the Dungey-cycle is critical in the formation of open tail lobes, which, at Jupiter, extend anti-sunward of the planet by several AU to roughly the orbit of Saturn (Behannon et al., 1983; Cowley et al., 2003b). It is nevertheless important for an overall understanding of the nature of these systems to compare quantitatively the flux transport due to these processes, such that we can assess, for example, the contribution of the Dungey-cycle return flows to the equatorial transport in the outer magnetosphere. These topics are conveniently discussed in terms of the relative volt-ages associated with the motional electric field E=−v×B due to these flow systems, where v is the plasma velocity and B the magnetic field, since by Faraday’s law a voltage of 1 V corresponds to a flux transport of 1 Wb s−1. In this section
we thus first review recent results concerning the Dungey-cycle voltage at Jupiter and Saturn, and then compare them with estimates of the flow driven by planetary rotation. 3.1 Flux transport associated with Dungey-cycle flow Until recent times only rather crude spot estimates had been made of the magnetopause reconnection rates that initiate the Dungey-cycle at Jupiter and Saturn (e.g. Kennel and Coro-niti, 1975). Recently, however, more detailed estimates have been published, based on the growing collection of interplan-etary data obtained in the vicinity of the planinterplan-etary orbits by the Ulysses and Cassini spacecraft (Jackman et al., 2004; Nichols et al., 2006). These studies employed an empirical formula for the magnetopause reconnection voltage in terms of upstream interplanetary parameters, which was validated and adapted from studies at the Earth (e.g. Perrault and Aka-sofu, 1978; Milan et al., 2004), given by
VDC = vSWB⊥L0cos4(θ/2) . (1)
Here vSW is the velocity of the solar wind, B⊥ is the mag-nitude of the interplanetary magnetic field (IMF) vector per-pendicular to the flow, and θ is the “clock angle” of this vec-tor measured from the planet’s north magnetic axis projected onto a plane perpendicular to the planet-Sun line. Length L0is then such that the field-perpendicular width of the
so-lar wind channel which reconnects with the planetary field is given by L0cos4(θ/2). This width is a maximum equal
to L0 when θ =0◦ i.e. when the IMF points northward
op-posite to the equatorial planetary field, and falls to small values beyond θ ∼90◦. From a study of reconnection rates at Earth, Milan et al. (2004) found a value for the scale length L0∼5 RE i.e. approximately half the sub-solar mag-netopause stand-off distance. For Jupiter and Saturn L0has
therefore been scaled according to the size of the magneto-spheres, such that L0∼30RJ (on average) at Jupiter, while
L0∼10 RSat Saturn.
The interplanetary medium at the orbital distances of Jupiter and Saturn typically exhibits strong variations during each ∼25-day solar rotation due to the effect of both coro-tating interaction regions (CIRs) and coronal mass ejection (CME) events. As a consequence, the reconnection voltages estimated from Eq. (1) show corresponding strong temporal variations over such intervals due principally to changes in the strength of the IMF, upon which further modulation is superposed at shorter periods due to the clock angle effect. Lowest field strengths and voltages occur during several-day CIR rarefaction regions during which the solar wind speed falls with time, while highest field strengths and voltages occur during few-day CIR compression regions when the solar wind speed increases (usually across paired shocks) and during few-day CMEs. Considering first the results for Jupiter, Nichols et al. (2006) studied three extended intervals of Ulysses data as the spacecraft flew near Jupiter’s orbital path during 1992, 1998 and 2004, and one further interval
of data obtained by Cassini during its fly-by of Jupiter at the end of 2000. The data thus span a complete solar cy-cle, though the variations over the cycle were found to be relatively modest. Typical magnetopause reconnection volt-ages were estimated to be VDC∼150 kV during rarefaction regions, which occur ∼90% of the time, increasing by an or-der of magnitude to VDC∼1MV during CIR compressions and CMEs, which occur ∼10% of the time (i.e. in one or two intervals of ∼2–3 days total duration during each so-lar rotation). These and subsequent voltage values are listed in Table 1, for purposes of comparison. The open flux pro-duced during the extended rarefaction intervals integrates to ∼300 GWb over one solar rotation, while that produced in the relatively short-lived compression regions integrates to ∼200 GWb. The total open flux produced over a solar rota-tion is thus ∼500 GWb, corresponding to an overall average magnetopause reconnection rate of ∼250 kV. Since the jo-vian magnetotail contains ∼300–500 GWb of flux per lobe, the averaged tail flux replenishment time is thus estimated to be ∼15–25 days, with a consequent tail length of ∼4–6 AU consistent with the above discussion.
Considering now the case for Saturn, Jackman et al. (2004) employed a ∼6-month interval of interplanetary data mea-sured by Cassini as it approached Saturn at the start of 2004, corresponding to the declining phase of the solar cycle. Their results (again listed in Table 1) indicate typical reconnection voltages of VDC∼25 kV during rarefaction regions, which occur ∼85% of the time, increasing to VDC∼150 kV dur-ing CIR compressions, which occur ∼15% of the time (i.e. one or two intervals of ∼4 days total duration during each solar rotation). The open flux produced during rarefaction regions then integrates to ∼50 GWb in each solar rotation, while that produced in compression regions also integrates to ∼50 GWb. The total amount of open flux created is then ∼100 GWb per solar rotation, corresponding to an averaged magnetopause reconnection rate of ∼45 kV. Since the kro-nian magnetotail contains ∼25–40 GWb of open flux per lobe, the averaged tail flux replenishment time is estimated to be ∼6–10 days, with a consequent tail length of ∼1.5– 2.5 AU.
It should be noted here that the values determined above using Eq. (1) are estimates of the reconnection rate at the magnetopause, while we are particularly interested in the Dungey-cycle contribution to flux transport on closed field lines in the outer magnetosphere following reconnection in the tail, as depicted in Fig. 1. It is firstly evident that the av-eraged Dungey-cycle tail reconnection rate, and consequent closed flux transport rate in the outer magnetosphere, must be equal to the averaged magnetopause reconnection rate, estimated above to be ∼250 kV at Jupiter and ∼45 kV at Saturn. Beyond this it seems reasonable to assume that the tail reconnection rate approximately follows the variations in the magnetopause reconnection rate during each solar rota-tion, such that the averaged tail reconnection rate at Jupiter would be ∼150 kV during rarefaction regions, increasing to
∼1 MV during CIR compression regions and CMEs. The corresponding values for Saturn are ∼25 kV for rarefaction regions and ∼150 kV for compressions, in good agreement with the findings of Badman et al. (2005) based on analy-sis of auroral data from the January 2004 Cassini-HST cam-paign. In addition to this, however, we note that at Earth tail reconnection tends to be impulsive, resulting in substorms and other nightside flow burst phenomena that may be trig-gered internally or by interplanetary events (e.g. Lyons et al., 1997; Boudouridis et al., 2003, 2004; Milan et al., 2006). The consequence is that while the magnetopause reconnec-tion rate at Earth, averaged over all interplanetary condireconnec-tions, is ∼30 kV, the typical tail reconnection rate, when it occurs, is ∼90 kV, lasting for about one third of the time (Milan et al., 2004, 2006). It should therefore be recognised that the typ-ical tail reconnection rates at Jupiter and Saturn, when they do occur, may be higher than the magnetopause reconnec-tion rates estimated above, but lasting for correspondingly shorter intervals. If a similar factor of three applies at Jupiter as at Earth, for example, the tail reconnection rate might be ∼3 MV during compression regions, though occurring for a total of only ∼1 day during each solar rotation. Similarly, the tail reconnection rate at Saturn might be ∼450 kV, occurring for a total of ∼1.5 days per solar rotation according to the above discussion.
3.2 Flux transport associated with rotational flow and com-parison with the Dungey-cycle
We now consider the flux transport driven by the planetary rotation and compare it with that due to the Dungey-cycle flows considered above. If planetary magnetic flux 8 ro-tates at angular velocity ω, such that the rotation period is T =2πω, then the rotational flux transport and voltage as-sociated with the flow is given by
VROT=
8
T =
8 ω
2π . (2)
Generally the plasma will sub-corotate at a fraction k of the planet’s angular velocity P, such that ω=k P, where for sub-corotation 0<k<1. We then have
VROT= k 8 P 2 π = k 8 TP , (3)
where TP=2πP is the planetary rotation period. Previ-ous simple estimates of the rotational voltage have gener-ally considered the whole of the planetary flux over a given hemisphere and have assumed rigid corotation (k=1), as will initially be assumed here. To estimate the amount of flux in one hemisphere we integrate the principal dipole compo-nent of the internal planetary field over the hemisphere. For Jupiter we use the VIP-4 jovian magnetic field model de-rived by Connerney et al. (1998) to estimate the total hemi-spheric magnetic flux to be ∼14 000 GWb, such that for rigid corotation with a ∼9.9 h rotation period, the associated flux
Table 1. Summary of estimated Dungey-cycle and rotational voltages for Jupiter and Saturn.
Voltage estimates Jupiter (MV) Saturn (MV) Rotational voltage (total) 400 12
Rotational voltage (middle magnetosphere or ring current region) 2.5 0.4–0.6 Rotational voltage (outer magnetosphere) 2–4 0.18 Dungey-cycle voltage (compression region) 1 0.15 Dungey-cycle voltage (rarefaction region) 0.15 0.025 Dungey-cycle voltage (average) 0.25 0.045
transport is VROT∼400 MV (Table 1). Similarly, using the
Cassini model of Saturn’s magnetic field (Dougherty et al., 2005), we find that at Saturn the total hemispheric magnetic flux is ∼480 GWb, so that with a ∼10.8 h rotation period we obtain VROT∼12 MV (Table 1). It may be thought that
these voltage values represent overestimates since the plasma sub-corotates throughout much of the outer magnetosphere. However, this sub-corotation region maps to within ∼20◦of the magnetic pole at Jupiter and within ∼25◦of the pole at Saturn, corresponding to only ∼10% and 20%, respectively, of the total planetary magnetic flux (Cowley et al., 2004b, 2005b), as will be discussed further below. If the plasma rotates on average at approximately half the planetary angu-lar velocity throughout this region, then the above rotational voltage estimates will be reduced by only ∼5% and 10%, respectively, due to this effect. These considerations thus produce only minor corrections to the above total rotational voltage values.
It is thus evident that these rotational voltages very greatly exceed the averaged Dungey cycle flux transports discussed above. Even the estimated compression region Dungey-cycle voltages at Jupiter and Saturn are only ∼1% of these val-ues, or less, which may be taken to imply that the Dungey-cycle flows are quite negligible at these planets, except for the production of the extended magnetotail. By comparison, the rotational voltage at Earth computed on the same basis
is VROT∼90 kV. The average 30 kV Dungey-cycle
reconnec-tion rate in this case is already 30% of the rotareconnec-tional voltage, while the typical rate of tail reconnection, when it occurs, is comparable or larger. We therefore see that the magneto-spheres of Jupiter and Saturn are very similar to each other in this respect, but are very different to the magnetosphere of the Earth.
This conclusion on the negligible role of the Dungey-cycle flows at Jupiter and Saturn considerably overstates the case, however, since most of the rotating flux considered above closes in the quasi-dipolar inner regions of the magneto-sphere where the fields are strongest. As indicated above, the flux circulating in the outer parts of these magnetospheres is generally a small fraction of the total, and also usually signif-icantly sub-corotates relative to the planet, leading to greatly reduced rotational voltage values for these regions. It may
still be the case, therefore, that the Dungey-cycle contributes significantly to the flux transport in the outer regions of these magnetospheres as shown in Fig. 1. To investigate this issue we will now make some estimates of the rotational flux trans-port specifically in the outer regions of Jupiter’s and Saturn’s magnetospheres, considering both the middle magnetosphere or “ring current” regions where strong azimuthal currents are present, and the “outer magnetosphere” layer adjacent to the magnetopause where the Vasyliunas-cycle and the Dungey-cycle return flow takes place, according to Fig. 1. We be-gin with Jupiter and first consider the rotational flow in the middle magnetosphere, which we take to extend across the region from where corotation breaks down at ∼20 RJ radial distance to the outer edge at ∼60 RJ. Using the Khurana and Kivelson (1993) model of the equatorial magnetic field, the amount of magnetic flux threading this region is estimated to be ∼160 GWb. The typical plasma angular velocity in this region based on Voyager and Galileo spacecraft data corre-sponds roughly to k=0.6 (e.g. Kane et al., 1995; Krupp et al., 2001) such that from Eq. (3) we obtain an estimate of the rotational voltage in Jupiter’s middle magnetosphere (sub-script “MM”) of VROT MM∼2.5 MV (Table 1). This value is
also in agreement with the theoretical model calculation by Nichols and Cowley (2005), which yields VROT MM∼3 MV
across the same region. We can also estimate the rotational voltage across Jupiter’s outer magnetosphere layer, which ex-tends from the outer edge of the middle magnetosphere to the magnetopause in the dayside sector of the magnetosphere (see Fig. 1). Since this flux does not complete a full rotation of the planet, such that Eq. (3) is not evidently appropriate, we instead estimate the voltage by integrating the motional electric field EOM across the outer magnetosphere layer to obtain
VROT OM≈ EOMLOM ≈ vOMBOMLOM, (4)
where vOM is the velocity of the plasma, BOM is the outer magnetosphere field strength, and LOM is the width of the layer. Spacecraft observations show that the outer magneto-sphere layer is ∼15 RJ wide adjacent to the dayside mag-netopause, with a field strength of ∼10 nT (e.g. Acu˜na et al., 1983). The velocity of the plasma in this region is typically vOM∼200−400 km s−1(i.e. k∼0.25–0.5), possibly
depending on the state of expansion of the magnetosphere (e.g. Kane et al., 1995; Krupp et al., 2001). From Eq. (4) we then find the voltage associated with the rotational flow in the outer magnetosphere is VROT OM∼2−4 MV (Table 1).
Com-paring the voltage values in Table 1 it is thus evident that rar-efaction region Dungey-cycle voltages of VDC∼150 kV are still small compared with these rotational voltages in both the middle and outer regions of the magnetosphere. However, compression region Dungey-cycle voltages of VDC∼1 MV, although occurring only ∼10% of the time, are directly com-parable in magnitude with those of the rotational flow in both the middle and outer magnetosphere. When such volt-ages occur, possibly further augmented by the impulsive tail behaviour discussed above, the Dungey-cycle flows will contribute significantly to the flow in the outer regions of Jupiter’s magnetosphere.
Similarly for Saturn’s magnetosphere, we first examine the rotational flows in the ring current region, analogous to the middle magnetosphere at Jupiter. Pioneer-11 and Voy-ager observations show that this extends from an inner edge at ∼6–8 RS out to distances of ∼16 RS (Connerney et al., 1983; Bunce and Cowley, 2003; Cowley and Bunce, 2003; Cowley et al., 2004b). Cowley et al. (2004b) used a mag-netic field model based on Voyager data to show that the amount of magnetic flux threading the equatorial plane be-tween these radial limits is ∼25–40 GWb. Voyager data show that the typical plasma angular velocity in this region corre-sponds to k∼0.6 (Richardson, 1986; Richardson and Sittler, 1990). From Eq. (3) we then find that the voltage associ-ated with the rotational flow in Saturn’s ring current region is VROT RC∼400−600 kV (Table 1). For the outer
magneto-sphere, the layer between the outer edge of the ring current region and the magnetopause, we again use Eq. (4) with a width LOM∼6 RS(e.g. Arridge et al., 2006), a field strength BOM∼5 nT (e.g. Dougherty et al., 2005), and a flow speed of
v∼100 km s−1corresponding to k∼0.7 (Richardson, 1986;
Richardson and Sittler, 1990; Szego et al., 2005; Hartle et al., 2006). Equation (4) then yields an outer magnetosphere rotational voltage of VROT OM∼180 kV (Table 1).
Compar-ing these values with those for the Dungey-cycle at Saturn given in Table 1 shows that, as at Jupiter, these rotational voltages are much larger than the rarefaction region Dungey-cycle voltages, estimated to be VDC∼25 kV. However, the compression-region Dungey-cycle voltages of ∼150 kV are again competitive, especially if augmented by impulsive tail behaviour, such that when these peak voltages are occurring, the Dungey-cycle flow will have a significant influence in the outer magnetosphere.
To take the argument a step further, we can compute the radial width of the layer that the Dungey-cycle “return” flow contributes to the outer magnetosphere region adjacent to the dawn magnetopause, as depicted in Fig. 1. Following Eq. (4), the voltage across the layer is VDC≈EOMLDCwhere EOM is the electric field associated with the flow, and LDC is the layer width perpendicular to the magnetopause. If the plasma
flow velocity in the layer is vOM, and the magnetic field strength adjacent to the magnetopause is BOM, as before, this becomes VDC≈vOMBOMLDC, such that
LDC ≈ VDC
vOMBOM
. (5)
Writing the flow velocity in terms of the planetary angular velocity, we have vOM=k RMPP=2π k RTPMP, where RMP is the magnetopause radius. Then Eq. (5) becomes
LDC ≈
VDCTP
2π k RMPBOM
. (6)
For rarefaction region conditions at Jupiter we use RMP∼90 RJ (Joy et al., 2002) in the pre-noon hours (e.g.
∼09:00 LT), k∼0.25, BOM∼5 nT, and VDC∼150 kV
(Ta-ble 1) to find LDC∼1 RJ, thus representing a minor con-tribution under these conditions. During CIR- or CME-related solar wind compressions of the magnetosphere, when
RMP∼60 RJ, k∼0.5, BOM∼10 nT, and VDC∼1 MV,
how-ever, we find LDC∼4 RJ, possibly augmented further if the tail reconnection is impulsive. This represents a more sig-nificant contribution to an outer magnetosphere layer of 10– 15 RJthickness under these conditions. Similarly, under rar-efaction region conditions at Saturn we use RMP∼30 RS in the pre-noon hours (Arridge et al., 2006), k∼0.7 (Richard-son, 1986; Richardson and Sittler, 1990; Szego et al., 2005; Hartle et al., 2006), and BOM∼4 nT (Dougherty et al., 2005), to obtain a layer width LDC∼0.5 RS when VDC∼25 kV. Under compression region Dungey-cycle conditions when
VDC∼150 kV we use RMP∼20 RS, k∼0.7, and BOM∼10 nT
to obtain LDC∼2 RS, which again may be augmented if tail reconnection is impulsive. As at Jupiter, the layer width un-der rarefaction region conditions at Saturn is small and es-sentially negligible, but under compression region conditions it becomes a significant contributor to the outer magneto-sphere. We note that similar hot plasma layer widths adja-cent to Saturn’s magnetopause have been estimated on the basis of auroral distributions by Badman et al. (2006).
4 Identification of Dungey-cycle flows in the equatorial magnetosphere
The above discussion indicates that under conditions of peak Dungey-cycle tail reconnection rates associated with inter-planetary CIR compressions or CMEs, equatorial “return” flow layers of non-negligible width should exist adjacent to at least the pre-noon magnetopauses at Jupiter and Sat-urn. The layer may become thinned in the post-noon hours, however, if significant reconnection-related flux tube erosion is present at the dayside magnetopause, as indicated in the steady-state picture shown in Fig. 1. It is then of interest to consider how such layers may be identified, relative to outer magnetosphere flow layers associated with rotational dynamics and the Vasyliunas-cycle. Although not mentioned
in the works cited above in which this model has previously been discussed (Cowley et al., 2003b; 2004a, b), a key dif-ference exists between these layers which could in princi-ple allow their experimental identification. This concerns the differing sources of the hot plasma within these layers, which should result in a strongly different hot ion composi-tion. Since the sub-corotational middle magnetosphere re-gion and Vasyliunas-cycle flows are driven specifically by internal sources combined with planetary rotation, the ion component of these plasmas will be determined by the na-ture of the internal sources gases. At Jupiter, therefore, this internal plasma will be dominated by sulphur and oxygen ions originating from Io (e.g. Bagenal, 1994; Radioti et al., 2005), while at Saturn it will be dominated by oxygen and hydrogen originating from the icy moons (e.g. Young et al., 2005). The hot plasma in the Dungey-cycle “return” region, however, results from the heating of tail lobe plasma down-stream from the tail reconnection site, and will thus consist principally of light ions, hydrogen and helium, originating either from the planet’s ionosphere via the polar wind (po-tentially containing singly-charged helium), or from the solar wind (containing doubly-charged helium).
We can also estimate the temperature of the heated ions within the outer magnetosphere layer. When reconnection occurs in the tail current sheet, either on closed field lines during the Vasyliunas-cycle, or on open field lines during the Dungey-cycle, the newly-closed reconnected field lines con-tract towards the planet. The ions on the concon-tracting field lines are accelerated approximately to the Alfv´en speed out-side the current sheet, VA=B/√µ0mini, where B is the field strength outside the current sheet, and mi and ni are the ion mass and number density respectively (e.g. Cowley, 1984). If we assume that the plasma is composed of a single ion species (the dominant contributor to the mass density) then the energy of these ions following acceleration will be
Wi ≈ 1 2miV 2 A ≈ 1 2 B2 µ0ni . (7)
The energy per ion thus depends only on the field strength and number density, and not on the ion mass. Consider-ing first the jovian tail current sheet at radial distances of ∼100 RJ where B∼6 nT and ni∼0.01 cm−3(e.g. Russell et al., 1998; Frank et al., 2002; Kronberg et al., 2005), we obtain from Eq. (7) an ion energy of ∼10 keV. This value is in agreement with ion temperatures in the current sheet presented by Frank et al. (2002). As the plasma is trans-ported from the tail towards the dayside, its energy may be augmented by factors of ∼2–3 due to adiabatic compres-sion of the contracting flux tubes, such that we then expect the production of a hot-ion plasma with temperatures of a few tens of keV in the dayside outer magnetosphere, both in the Dungey-cycle and the Vasyliunas-cycle layers. Con-sidering now Saturn’s magnetotail at a distance of a few tens of RS from the planet, we take values of B∼3 nT and
ni∼0.01 cm−3(Ness et al., 1981; Richardson, 1986) to ob-tain using Eq. (7) an ion energy of ∼2 keV. Again, this energy may be augmented by factors of ∼2–3 due to adiabatic com-pression of the plasma as it rotates round to the dayside mag-netosphere, such that we anticipate hot ion layers of ∼5 keV energy in the dayside outer magnetosphere in this case.
Thus to the extent that cross-field diffusion does not “blur” the ion composition, it should be possible to identify Dungey-cycle “return” flows in the outer magnetospheres of Jupiter and Saturn, and to distinguish them from regions dominated by the dynamics associated with the transport of plasma from internal sources, by examination of the domi-nant ion species at energies from a few keV to a few tens of keV. According to Fig. 1, the Dungey-cycle flows should form a hot-plasma layer adjacent to the magnetopause in the pre-noon hours if magnetopause reconnection is on-going, but will be more broadly distributed across the dayside re-gion including the dusk sector if it is not. Similar comments apply to the layers of antisunward flow tailward of the re-connection sites in the centre plane of the tail. The tailward-flowing plasma sheet associated with the Dungey-cycle and the closure of open lobe flux on the dawn flank will consist primarily of light ions with ∼ keV energies, while that as-sociated with the tailward-propagating plasmoid formed by the Vasyliunas-cycle will consist principally of heavy ions with similar energies. As indicated above, however, Kivel-son and Southwood (2005) have recently speculated that the nightside outflow in Jupiter’s magnetotail is associated with sequential outflow events that involve episodes of plasmoid ejection and open flux closure on much smaller spatial scales than is envisaged in Fig. 1. In this case the Vasyliunas-cycle and Dungey-cycle “return” flows may become inextricably interlinked, such that no separate flow components with in-dividual ion composition signatures may occur.
With regard to observations, we note that no directly rele-vant data concerning the composition of ions at energies of a few keV to a few tens of keV per ion have yet been published for the outer magnetosphere regions of either Jupiter or Sat-urn. This paper therefore sets out the groundwork for future experimental tests of the ideas on magnetospheric structure and dynamics at these giant planets, outlined in Fig. 1. Un-fortunately it appears unlikely that definitive information can be derived for Jupiter’s outer magnetosphere from existing data from the Galileo orbiter. The reader is referred to pub-lications by e.g. Frank et al. (2002) and Frank and Paterson (2004) for discussion of the limitations in ion mass resolu-tion of the Galileo instrumentaresolu-tion in the above energy range. Mass-resolved ion data is available from Galileo, but at en-ergies of typically hundreds of keV per ion (e.g. Radioti et al., 2005), corresponding to the high-energy tail of the ther-mal populations of central interest here. The anisotropies of these energetic ions have been employed to study the flows in Jupiter’s magnetosphere (e.g. Krupp et al., 2001; Woch et al., 2004), and have been used to identify flow bursts in the jo-vian tail attributed to mass-release and the Vasyliunas-cycle
(Woch et al., 1999; Kronberg et al., 2005). At Saturn, hot plasma injections from the magnetotail have been observed by Cassini energetic neutral atom imaging data by Mitchell et al. (2005), and have been attributed to tail reconnection similar to substorms at Earth. These data include supra-thermal fluxes of mass-resolved hydrogen and oxygen at en-ergies from several tens to a few hundred keV, again above the thermal ion energy range estimated here. Mass-resolved ion data at thermal energies should also become available from the Cassini plasma spectrometer (Young et al., 2004), but these observations may be difficult at the thermal plasma densities envisaged here (few times 0.01 cm−3). Neverthe-less we hope that the theoretical discussion given here con-cerning the physical significance of such observations will provide impetus for detailed future studies of such data.
5 Summary
In this paper we have considered the contribution of the so-lar wind-driven Dungey-cycle to flux transport in the closed field regions of Jupiter’s and Saturn’s magnetospheres. Our estimates of the Dungey-cycle voltage in these systems have been derived from recent studies based on spacecraft mea-surements of the interplanetary medium near the orbits of these planets, combined with an empirical formula for the magnetopause reconnection rate validated at Earth. These values have then been compared with the voltages associated with the flows driven by planetary rotation. While the tradi-tional comparison with the voltage associated with the rota-tional transport of the total planetary magnetic flux indicates that Dungey-cycle flows are negligible in these systems, be-ing at most ∼1% of the rotational transport, here we point out that most of this rotational transport takes place in the innermost part of the system where the fields are strongest. If instead we consider only the rotational flows associated with the middle and outer regions of these magnetospheres, we find that while they are still more than an order of mag-nitude larger than the averaged Dungey-cycle voltages, and those occurring during solar wind rarefaction regions, they are of the same order as the typical Dungey-cycle voltages occurring in these systems during CIR compression regions and CMEs, namely ∼1 MV at Jupiter and ∼150 kV at Sat-urn. Under such conditions, therefore, the Dungey-cycle contributes a significant transport of magnetic flux within the outer parts of the closed field regions of these magne-tospheres. Specifically, the width of the Dungey-cycle “re-turn” flow layer inside the pre-noon dayside magnetopause is then estimated to be typically ∼4 RJ in Jupiter’s magne-tosphere and ∼2 RS in Saturn’s magnetosphere, occurring ∼10% of the time, compared with about one planetary ra-dius or less during rarefaction regions. Thicker layers may occur if the tail reconnection is impulsive, but then lasting for correspondingly shorter intervals of time.
We also suggest that it may be possible to experimentally identify such layers inside these magnetospheres through the hot ion composition, provided the “blurring” effect of cross-field particle diffusion is not too strong. While regions driven by planetary rotation should be dominated by heavy-ion plas-mas originating from internal moon sources, the Dungey-cycle layers should principally contain hot light ions originat-ing from either the planet’s ionosphere or the solar wind. Es-timates of the typical ion temperatures at Jupiter are ∼10 keV in the tail and ∼20–30 keV in the dayside outer magneto-sphere, while for Saturn the energies are ∼2 keV in the tail and ∼5 keV ion the dayside outer magnetosphere.
Acknowledgements. Work at Leicester was supported by PPARC
grant PPA/G/O/2003/00013. S. V. Badman was supported by a PPARC Quota Studentship, and S. W. H. Cowley by a Royal So-ciety Leverhulme Trust Senior Research Fellowship.
Topical Editor I. A. Daglis thanks I. Dandouras and another ref-eree for their help in evaluating this paper.
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